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Patterns created from copies of a single piece which exhibit every possible symmetry for the grid. The first column contains the Baiocchi figures with maximal symmetry, and the last has the patterns which have no overall symmetry. In each case the example shown has the fewest pieces so that the pattern displays no higher symmetries. Patterns marked * courtesy George Sicherman.

 

Monogem

Full	Sextarotary	Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Horizontal	Vertical	Birotary	None
									*

Digems

Full	Sextarotary	Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Horizontal	Vertical	Birotary	None
				*
		*

Trigems

Full	Sextarotary	Ternary & Horizontal	Ternary & Vertical	Trirotary	Double Bilateral	Horizontal	Vertical	Birotary	None
		*
		*
		*
		*
			*
									*
			*		*		*
	*
									*
			*		*
	*